Many of the unique properties of metallic nanoparticles are determined not only by their finite size but also by their shape, defined by the crystallographic orientation of the surface facets. These surfaces (and therefore the nanoparticles themselves) may differ in a number of ways, including surface atom densities, electronic structure, bonding, chemical reactivities, and thermodynamic properties. In the case of gold, it is known that the melting temperature of nanoparticles strongly depends on the crystal size and that the shape may alter considerably (and yet somewhat unpredictably) during annealing. In this work we use first principle calculations and a thermodynamic model to investigate the morphology of gold nanoparticles in the range 3-100 nm. The results predict that the equilibrium shape of gold nanoparticles is a modified truncated octahedron and that the (size-dependent) melting of such particles is preceded by a significant change in the nanoparticle's morphology.